1 A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three programmers?

A 1 year
Author(s): The Open University

1 Which is greater, 1.2 minutes or 70 seconds?

There are at least three ways of answering this:

• (a) 70 seconds is
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1 Convert each of the following fraction ratios to decimal ratios.

• (a) Author(s): The Open University

Although ratios are often given as fractions, they can also be expressed as decimals. You need to deal with a mixture of fractions and decimals, and to compare ratios given in either form, so you need to be able to convert between the two forms.

## Example 4

The ratio of the circumference of a cir
Author(s): The Open University

1 A local supermarket sells a popular breakfast cereal in a ‘Large Pack’ and ‘New Extra Large Pack’. They are both being sold at ‘knock down’ prices. The large pack contains 450 g of cereal priced at £1.85. The new extra large pac
Author(s): The Open University

Time conversions are also ratios. The ratio of time measured in minutes to time measured in seconds is one to sixty (1:60), as there are sixty seconds in a minute.

## Example 2

Adam's grandfather ran a mile in Author(s): The Open University

1 A friend is painting the inside walls of a garage. So far she has used a 2 litre tin of emulsion paint and covered an area of 9 m2. She needs some more paint. How much more would you advise her to purchase if she intends to pa
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To make short crust pastry, one recipe book says ‘use one part of fat to two parts of flour’; another recipe says ‘use fat and flour in the ratio of one to two’; and yet another says ‘use half as much fat as flour’. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

Author(s): The Open University

Ratios crop up often in official statistics. The government wants the teacher–pupil ratio in schools to be increased to one teacher to thirty pupils or less. The birth rate has fallen: the ratio of children to women of child bearing age has gone down. It used to be 2.4 to 1, and now it is 1.9 to 1. Predictions for the ratio of working adults to retired adults is disturbing. Predictions are, that by 2030 the ratio will be two working adults to every retired person, instead of three to one no
Author(s): The Open University

By the end of this unit you should be able to:

• work with simple ratios;

• convert between fractions, decimals and percentages;

• explain the meaning of ratio, proportion and percentage;

• find percentages of different quantities;

• calculate percentage increases and decreases;

• calculate average speeds in given units and find speeds, distances and times for travel at constant speed;

• convert units;
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The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

All written material contained within this unit originated at the Open University.

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We will now discuss complex numbers and their properties. We will show how they can be represented as points in the plane and state the Fundamental Theorem of Algebra: that any polynomial equation with complex coefficients has a solution which is a complex number. We will also define the function exp of a complex variable.

Earlier we mentioned several sets of numbers, including Author(s): The Open University

We need not restrict ourselves to rectangles: we can also build surfaces by identifying edges of other polygons. For example, if we start with a pentagon and identify two pairs of its edges as shown in Figure 33, what do we get? Identifying the edges labelled a and c in the directions indicated, we obtain
Author(s): The Open University

The final surface that can be obtained by identifying edges of a rectangle is even more complicated. Again it cannot be constructed in three dimensions, so is not a surface in space and is hard to visualise. This time we identify both pairs of opposite edges of the rectangle in opposite directions, as indicated by the arrowheads in Author(s): The Open University

The simplest example of a paper-and-glue construction is to make a rectangle into a cylinder by gluing together two opposite edges. We take a closed rectangle ABB' A' in the plane and identify the opposite edges AB and A'B', as shown in Figure 27. This means that:

Author(s): The Open University

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. When prompted to watch the video for this unit, return to this page and watch the clips below. After you've watched the clips, return to the workbook.

Click 'View document' to open the workbook (PDF, 0.3 MB).

Design
This unit looks at the process of design – from assessing the complexity of design as an activity, to exposing the difficulty in making general conclusions about how designers work. You will be able to identify innovation in a wide variety of designed objects and evaluate the impact of this innovation. First published on Wed, 27
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"DMC Upside": GIS Day
Del Mar College, Texas A&M University-Corpus Christi, Texas A&M University-Kingsville and the National Geospatial Technology Center of Excellence at Del Mar College hosted "Discovering the World Through GIS" on Nov. 15, 2012. The local event is part of the National Geographic Society's Geography Awareness Week (Nov. 12-18), which includes GIS Day. This segment of the "DMC Upside" television program was featured in the December 2012 edition, which airs on cable channel 19 in Corpus Christi. The
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Systems Thinking
Linda Vanasupa
This set of learning materials is aimed at explaining and fostering the discipline of systems thinking.
Some Rights Reserved

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EndNote X6 for MAC
EndNote X6 for MAC - L M Robertson Keywords:EndNote , Bibliography , Referencing , Resource Management , Managing references , MAC <
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